Đáp án:
Giải thích các bước giải:
1) `\sqrt{2x-3}-3(2x-3)=0`
ĐK: `x \ge 3/2`
`⇔ \sqrt{2x-3}=3(2x-3)`
`⇔ 2x-3=9(2x-3)^2`
`⇔ 2x-3=9(4x^2-12x+9)`
`⇔ 2x-3=36x^2-108x+81`
`⇔ 36x^2-110x+84=0`
`⇔ (2x-3)(9x-14)=0`
`⇔` \(\left[ \begin{array}{l}x=\dfrac{3}{2}\\x=\dfrac{14}{9}\end{array} \right.\) (TM)
Vậy `S={3/2;14/9}`
2) `\sqrt{x-2}-5\sqrt{x^2-4}=0`
ĐK: \(\begin{cases} x-2 \ge 0\\ x^2-4 \ge 0\end{cases}\)
`⇔` \(\begin{cases} x \ge 2\\ \left[ \begin{array}{l}x \ge 2\\x \le -2\end{array} \right.\end{cases}\)
`⇒ x \ge 2`
`⇔ \sqrt{x-2}=5\sqrt{x^2-4}`
`⇔ x-2=25(x^2-4)`
`⇔ x-2=25x^2-100`
`⇔ 25x^2-x-98=0`
`⇔ (x-2)(25x+49)=0`
`⇔` \(\left[ \begin{array}{l}x = 2\ (TM)\\x = -\dfrac{49}{25}\ (L)\end{array} \right.\)
Vậy `S={2}`
3) `\sqrt{y-3}+1/5 \sqrt{25y-75}-1/6 \sqrt{9y-27}=8`
ĐK: `y \ge 3`
`⇔ \sqrt{y-3}+1/5 \sqrt{25y-75}-1/6 \sqrt{9y-27}=8`
`⇔ \sqrt{y-3}+1/5 \sqrt{25(y-3)}-1/6 \sqrt{9(y-3)}=8`
`⇔ \sqrt{y-3}+1/5 . 5\sqrt{y-3}-1/6 . 3\sqrt{y-3}=8`
`⇔ 3/2 \sqrt{y-3}=8`
`⇔ \sqrt{y-3}=\frac{16}{3}`
`⇔ y-3=\frac{256}{9}`
`⇔ y=283/9\ (TM)`
Vậy `S={283/9}`
4) `\sqrt{4x-20}+3\sqrt{x-5}-2/3 \sqrt{9x-45}=3`
DK: `x \ge 5`
`⇔ \sqrt{4(x-5)}+3\sqrt{x-5}-2/3 \sqrt{9(x-5)}=3`
`⇔ 2\sqrt{x-5}+3\sqrt{x-5}-2\sqrt{x-5}=3`
`⇔ 3\sqrt{x-5}=3`
`⇔ \sqrt{x-5}=1`
`⇔ x-5=1`
`⇔ x=6\ (TM)`
Vậy `S={6}`
